Stochastic Distribution Processes with applications to Stochastic Differential Equations Driven by Lévy White Noise
Institution: | University of Oslo |
---|---|
Department: | |
Year: | 1000 |
Keywords: | VDP::410 |
Record ID: | 1284800 |
Full text PDF: | http://urn.nb.no/URN:NBN:no-26898 https://www.duo.uio.no/handle/10852/10158 https://www.duo.uio.no/bitstream/handle/10852/10158/1/MasteroppgaveElinERose.pdf |
We regard a stochastic process as a weakly measurable function, taking values one of the Kondratiev Stochastic distribution spaces, (S)_{-\rho}. Since these spaces are duals of nuclear spaces, functions taking values in the dual of a nuclear space are treated in detail. The space (S)_{-1} is a topological algebra with respect to the Wick product, ⋄, and the following relation hold, ∫Y(s)δη(s)=∫Y(s)⋄\dot{η}(s)ds. As a consequence, we can regard SDEs as (S)_{-1}-valued ODEs. Similarily, we will regard an SPDE as an (S)_{-1}-valued PDE.